Details

Time bar (total: 10.1s)

sample26.0ms

Algorithm
intervals
Results
16.0ms266×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b
(* y (+ 1.0 (* z z)))
3.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
6.0ms
(* y (+ 1.0 (* z z)))
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series109.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(* y (+ 1.0 (* z z)))
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify52.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
4.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 frac-2neg clear-num associate-/r/ associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 264
Calls
2 calls:
5.0ms
(/ (/ 1.0 y) x)
17.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 y) x)
61.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify114.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011322994
145722919
250022919

prune754.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize29.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (cbrt (+ 1.0 (* z z))) (cbrt (+ 1.0 (* z z)))))
13.5b
(cbrt (+ 1.0 (* z z)))
13.5b
(cbrt (+ 1.0 (* z z)))
13.5b
(cbrt (+ 1.0 (* z z)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
121×add-exp-log
58×cbrt-undiv div-exp
47×add-cbrt-cube
37×prod-exp cbrt-unprod
21×times-frac
18×cbrt-div
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×cbrt-prod flip3-+ flip-+ associate-/l*
8×associate-/r/
5×div-inv
4×pow1 frac-times add-log-exp
3×pow1/3
2×associate-*r/ associate-*l/
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 121
Calls
4 calls:
20.0ms
(/ (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (cbrt (+ 1.0 (* z z))) (cbrt (+ 1.0 (* z z)))))
1.0ms
(cbrt (+ 1.0 (* z z)))
1.0ms
(cbrt (+ 1.0 (* z z)))
2.0ms
(cbrt (+ 1.0 (* z z)))

series765.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(/ (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (cbrt (+ 1.0 (* z z))) (cbrt (+ 1.0 (* z z)))))
174.0ms
(cbrt (+ 1.0 (* z z)))
167.0ms
(cbrt (+ 1.0 (* z z)))
170.0ms
(cbrt (+ 1.0 (* z z)))

simplify101.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08742462
137981873
250011715

prune473.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
2.2b
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
13.0b
(sqrt (+ 1.0 (* z z)))
13.0b
(sqrt (+ 1.0 (* z z)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
3216×times-frac
1886×add-sqr-sqrt
1326×add-cube-cbrt *-un-lft-identity
682×cbrt-prod
617×sqrt-prod
426×associate-*r*
245×associate-*l*
99×unswap-sqr
70×associate-/l*
67×add-exp-log
61×div-inv
51×add-cbrt-cube
36×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
8×pow1 sqrt-div
6×associate-/r*
5×associate-/r/
4×flip3-+ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1351
Calls
4 calls:
1.1s
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
28.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
119.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
49.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify276.0ms

Algorithm
egg-herbie
Counts
1363 → 1363
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0478426330
1500225983

prune4.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.4b

regimes262.0ms

Accuracy

0% (1.2b remaining)

Error of 6.0b against oracle of 4.9b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02329
12329

end0.0ms

sample744.0ms

Algorithm
intervals
Results
548.0ms8589×body80valid